I was firing my Jagdpanzer at a crew so I use T and then W as I only wanted to fire the BMG that is in slot 4. (I know about the slots).

Before I fired it the number of shots available was 3:-:4:5
After firing only the BMG the shots went to 2:-3:4

Before I fired I thought I had 3 shots with the 75mm, 4 with the Nahverteidigungswaffe, and then 5 with the BMG. But when I fired the BMG it subtracted 1 from each slot. So I am guessing I misunderstood the shot count system?

Each fire reduces the amount of shots in all slots regardless of whether that slot fired or not.
Shots represent the number of opportunities to fire the respective weapon in that game turn. Chosing not to fire 1 or 2 slots to save ammo means you lost the opportunity.

Think about it this represents the number of shots you can get off in the timeframe, the MG fires faster so gets more shots than the main gun. If you let each weapon take its shot individualy in this case the unit could fire 12 times in the turn.
If you let it fire normaly using all weapons it still has 12 shots but uses them in 5 fires.